Categoricaldata.net

Introduction

The world runs on information, but what is it? Information seems to have something
in common with mathematics: there are certain rules necessary to keep it consistent
and useful. We don't just mean information in Claud Shannon's sense---meaningless
data passing over a noisy channel---to us, information is meaningful, and that is
important. We want to know the operations one can perform that respect meaningful
information. As the mathematician Daniel Kan said, "Information is inherently a
combinatorial affair."

But what is the right mathematics for handling information? Information
lies on a spectrum, from chaotic to organized. Chaotic information, for
which a pattern needs to be found, should be handled by probabilistic or
machine-learning methods. But once something usable and known has been
extracted from the chaos, it should be organized algebraically, i.e.,
according to principled transformations that preserve its structure and
integrity. For this one should use category theory, the mathematics of
structure.

Category theory was designed to build bridges between different
conceptual landscapes. It has been very successful in doing so for the
field of mathematics, and we have reason to believe it will do so for
informatics as well. It does not unify, as if to create one world-view
to rule them all; instead it connects, allowing different disciplines to
remain distinct, but interoperable by way of a rigorous, flexible system
of translation.